The analysis of survival data is of considerable interest to studies in Division of Epidemiology, Statistics and Prevention Research and also to biomedical research in general as the data encountered is typically of that nature. Our objective in this project is multifold: (1) Develop methods to analyze time to an event which have non-standard type of incompleteness, that are beyond right censoring, like random truncation, current status and interval censoring. Extensive literature exists for dealing with data which are randomly right censored However, more effort is needed to develop methods to deal with other type of incompleteness which occur frequently. For example, random truncation is frequently observed in many retrospective pregnancy studies where women are enrolled in the study only if they have gotten pregnant by start of study. (2) Develop methods to deal with multivariate survival data. This part of the project is necessitated by needs of many epidemiological studies, where the interest is not just in modeling one simple event of interest, but rather a host of complex events. The focus of this part is to develop methods to analyze multivariate survival data like the multistage data, recurrent events and competing risks data. Examples of such multivariate data can be found in various studies being conducted in DESPR, NICHD like LIFE study and other prospective pregnancy studies, Safe Labor to name few. The methods developed here will address questions like modeling of progression of labot through various stages, modeling time to pregnancy to delivery or loss. Also, motivated by need to better understand the risk factors associated with women who suffer repeated adverse outcomes associated with pregnancy loss, we intend to study modeling such events using both the competing risks data as well as recurrent events data